Faster than light travel!

I'm reading Roger Penrose's The Emperor's New Mind. I'm less than halfway through, but so far the outline of the book seems to be
1) Review every major bit of math, physics, and metaphysics from the last 5000 years
2) Point out how the idea of determinism is pretty weak about 16 different ways
3) (and I haven't gotten to this point yet) show how a regular computer can never be a brain.

But the journey, in this case, is a good fraction of the fun. Today I read the twin paradox. I first learned this 35 years ago, I have known it in some sense for 2/3 of my life. And somehow in that time I never noticed that that Special Relativity allows for faster than light travel!

Consider this example to explain it. The space-faring twin leaves the earth, travels to a star 4.45 light-years away, and returns to earth. He does this at about 86% the speed of light, enough for about 50% time dilation.

The amazing thing, to me, is the traveling twin returns to earth after only 5.14 years of his own time have elapsed. So this twin woke up one day, said "I will leave on an 8.9 light-year trip today," and 5.14 years later looks up into the sky at the star 4.45 light-years away and says "I traveled to that star and back in 5.14 years." Indeed, he arrived at the star when only 2.57 of his subjective years had one by.

Now by my calculations, that twin traveled at 8.9/5.14 = 173% the speed of light!

And if he had traveled significantly faster than 86% c, he could have cut that elapsed time down to arbitrarily low.

Now this must have been true for the last 35 years, but how could I have not noticed it? How could I have not noticed that you can look out your window, see something 100 light years away, and if you can travel at .999999 c, you can get there in a very manageably short time?

I'm shocked and amazed at myself. And wondering, has this been exploited in science fiction? It seems it must have been. So how could I have not noticed it after reading all those thousands of sci fi books I ahve read?